Related papers: Phase Transition in Tensor Models

Tensor models are a generalization of matrix models (their graphs being dual to higher-dimensional triangulations) and, in their colored version, admit a 1/N expansion and a continuum limit. We introduce a new class of colored tensor models…

Ordinary tensor models of rank $D\geq 3$ are dominated at large $N$ by tree-like graphs, known as melonic triangulations. We here show that non-melonic contributions can be enhanced consistently, leading to different types of large $N$…

In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical…

We uncover a finite-time dynamical phase transition in the thermal relaxation of a mean-field magnetic model. The phase transition manifests itself as a cusp singularity in the probability distribution of the magnetisation that forms at a…

We investigate the critical properties of the phase transition towards complex tensor order that has been proposed to occur in spin-orbit coupled superconductors. For this purpose we formulate the bosonic field theory for fluctuations of…

This thesis focuses on renormalization of quantum field theories. Its first part considers three tensor models in three dimensions, a Fermionic quartic with tensors of rank-3 and two Bosonic sextic, of ranks 3 and 5. We rely upon the…

Amplitudes of ordinary tensor models are dominated at large $N$ by the so-called melonic graph amplitudes. Enhanced tensor models extend tensor models with special scalings of their interactions which allow, in the same limit, that the…

We consider a dynamical triangulation model of euclidean quantum gravity where the topology is not fixed. This model is equivalent to a tensor generalization of the matrix model of two dimensional quantum gravity. A set of moves is given…

Tensor models generalize random matrix models in yielding a theory of dynamical triangulations in arbitrary dimensions. Colored tensor models have been shown to admit a 1/N expansion and a continuum limit accessible analytically. In this…

Tensor models and tensor field theories admit a $1/N$ expansion and a melonic large $N$ limit which is simpler than the planar limit of random matrices and richer than the large $N$ limit of vector models. They provide examples of…

We study the thermodynamics of the linear sigma model with constituent quarks beyond the mean-field approximation. By integrating out the quark degrees of freedom we derive an effective action for the meson fields which is then linearized…

The dynamical triangulation model of three-dimensional quantum gravity is shown to have a line of transitions in an expanded phase diagram which includes a coupling mu to the order of the vertices. Monte Carlo renormalization group and…

We consider the quark-meson model with two quark flavors in a constant external magnetic field $B$ at finite temperature $T$ and finite baryon chemical potential $\mu_B$. We calculate the full renormalized effective potential to one-loop…

Recently a matrix model with non-pairwise index contractions has been studied in the context of the canonical tensor model, a tensor model for quantum gravity in the canonical formalism. This matrix model also appears in the same form with…

In this paper we analyze the multi-matrix model arising from the intermediate field representation of the tensor model with all quartic melonic interactions. We derive the saddle point equation and the Schwinger-Dyson constraints. We then…

Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random…

Continuum spacetime is expected to emerge via phase transition in discrete approaches to quantum gravity. A promising example is tensorial group field theory but its phase diagram remains an open issue. The results of recent attempts in…

In the group field theory approach to quantum gravity, continuous spacetime geometry is expected to emerge via phase transition. However, understanding the phase diagram and finding fixed points under the renormalization group flow remains…

Motivated in part by recent experiments on liquid crystals with bent-core molecules, which are observed to display a spontaneous chiral symmetry breaking, we introduce a field theory of a 3rd-rank tensor order parameter T^{ijk} to describe…

Mean-field theories of the glass transition predict a phase transition to a dynamically arrested state, yet no such transition is observed in experiments or simulations of finite-dimensional systems. We resolve this long-standing…